Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On model predictive control with sampled-data input for output tracking with prescribed performance

Dario Dennstädt, Lukas Lanza, Karl Worthmann

Abstract

We propose a model predictive control (MPC) scheme with sampled-data input which ensures output-reference tracking within prescribed error bounds for relative-degree-one systems. Hereby, we explicitly deduce bounds on the required maximal control input and sampling frequency such that the MPC scheme is both initially and recursively feasible. A key feature of the proposed approach is that neither terminal conditions nor a sufficiently-large prediction horizon are imposed, rendering the MPC scheme computationally efficient. We illustrate the MPC algorithm via a numerical example of a torsional oscillator.

On model predictive control with sampled-data input for output tracking with prescribed performance

Abstract

We propose a model predictive control (MPC) scheme with sampled-data input which ensures output-reference tracking within prescribed error bounds for relative-degree-one systems. Hereby, we explicitly deduce bounds on the required maximal control input and sampling frequency such that the MPC scheme is both initially and recursively feasible. A key feature of the proposed approach is that neither terminal conditions nor a sufficiently-large prediction horizon are imposed, rendering the MPC scheme computationally efficient. We illustrate the MPC algorithm via a numerical example of a torsional oscillator.
Paper Structure (7 sections, 3 theorems, 30 equations, 4 figures, 1 algorithm)

This paper contains 7 sections, 3 theorems, 30 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System class and control objective
  3. System class
  4. Control objective
  5. Sampled-data MPC
  6. Simulation
  7. Conclusion

Key Result

Theorem III.1

Consider system eq:Sys with $(f,g,\mathbf{T})\in\mathcal{N}^{m}$ and initial data $y^0\in\mathcal{C}([t_0-\sigma,t_0],\mathds{R}^m)$. Let $\psi\in\mathcal{G}$ and $\ y_{\mathop{\mathrm{ref}}\limits}\in W^{1,\infty}(\mathds{R}_{\geq0},\mathds{R}^{m})$. Then, there exists $u_{\max}>0$ and $\tau>0$ suc Furthermore, each global solution $x$ with corresponding input $u_{\rm MPC}$ satisfies:

Figures (4)

  • Figure 1: Error evolution in a funnel $\mathcal{F}_{\psi}$ with boundary $\psi(t)$; the figure is based on BergLe18a, edited for present purpose.
  • Figure 2: Torsional oscillator. The figure is based on Druecker22, edited to the case of two flywheels for the present purpose.
  • Figure 3: Outputs and reference, with error boundary.
  • Figure 4: Control inputs.

Theorems & Definitions (9)

  • Definition II.1
  • Remark II.1
  • Definition II.2
  • Definition III.1
  • Remark III.1
  • Remark III.2
  • Theorem III.1
  • Lemma 1.1
  • Corollary 1.1